The Annals of Probability

Normal approximation under local dependence

Louis H. Y. Chen and Qi-Man Shao

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We establish both uniform and nonuniform error bounds of the Berry–Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper than many existing ones in the literature. The proofs couple Stein’s method with the concentration inequality approach.

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Ann. Probab., Volume 32, Number 3 (2004), 1985-2028.

First available in Project Euclid: 14 July 2004

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G60: Random fields

Stein’s method normal approximation local dependence concentration inequality uniform Berry–Esseen bound nonuniform Berry–Esseen bound random field


Chen, Louis H. Y.; Shao, Qi-Man. Normal approximation under local dependence. Ann. Probab. 32 (2004), no. 3, 1985--2028. doi:10.1214/009117904000000450.

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